Methods and Devices for Decoding Quantum States

1. A method comprising: identifying, using one or more processors, lattice data having initial erasure portions and initial non-erasure portions; generating modified lattice data from the lattice data, wherein the modified lattice data comprises larger erasure portions that are larger than the initial erasure portions, and wherein the larger erasure portions include at least some of the initial non-erasure portions; generating output data by applying an erasure based decoding scheme to the modified lattice data; and storing the output data in memory.

2. The method of claim 1, wherein generating the modified lattice data comprises: merging the initial non-erasure portions, wherein merging the initial non-erasure portions forms additional erasure portions that are included in the larger erasure portions.

3. The method of claim 2, wherein the lattice data comprises a plurality of vertices that are connected by edges.

4. The method of claim 3, wherein the initial erasure portions comprise an even quantity of vertices, and the initial non-erasure portions comprise an odd number of vertices.

5. The method of claim 4, wherein the initial non-erasure portions having the odd number of vertices are merged to form the additional erasure portions, wherein the additional erasure portions have an even quantity of vertices.

6. The method of claim 2, further comprising: growing the initial non-erasure portions.

7. The method of claim 1, wherein the erasure based decoding scheme comprises a linear-time maximum likelihood erasure decoding scheme.

8. The method of claim 1, wherein the output data comprises one or more corrections for the larger erasure portions of the modified lattice data.

9. The method of claim 1, wherein the lattice data comprises lattice data of a quantum error correcting code.

10. The method of claim 1, wherein the lattice data comprises lattice data of a surface code.

11. The method of claim 1, wherein the lattice data comprises lattice data of a color code.

12. The method of claim 1, wherein erasure portions of the lattice data comprise qubit erasure data.

13. The method of claim 1, wherein non-erasure portions of the lattice data comprise Pauli error data.

14. A system comprising: one or more processors of a machine, a memory storing instructions that when executed by the one or more processors cause the machine to perform operations comprising: identify lattice data having initial erasure portions and initial non-erasure portions; generate modified lattice data from the lattice data, wherein the modified lattice data comprises larger erasure portions that are larger than the initial erasure portions, and wherein the larger erasure portions include at least some of the initial non-erasure portions; generate output data by applying an erasure based decoding scheme to the modified lattice data; and store the output data.

15. The system of claim 14, wherein generating the modified lattice data further comprises: merging the initial non-erasure portions, wherein merging the initial non-erasure portions forms additional erasure portions that are included in the larger erasure portions.

16. The system of claim 15, wherein the lattice data comprises a plurality of vertices that are connected by edges.

17. The system of claim 16, wherein the initial erasure portions comprise an even quantity of vertices, and wherein the initial non-erasure portions comprise an odd number of vertices.

18. The system of claim 17, wherein the initial non-erasure portions that have the odd number of vertices are merged to form the additional erasure portions, wherein the additional erasure portions have an even quantity of vertices.

19. A non-transitory machine-readable storage device embodying instructions that, when executed by a machine, cause the machine to perform operations comprising: identify lattice data having initial erasure portions and initial non-erasure portions; generate modified lattice data from the lattice data, wherein the modified lattice data comprises larger erasure portions that are larger than the initial erasure portions, and wherein the larger erasure portions include at least some of the initial non-erasure portions; generate output data by applying an erasure based decoding scheme to the modified lattice data; and store the output data.

20. The non-transitory machine-readable storage device of claim 19, wherein generating the modified lattice data comprises merging the initial non-erasure portions, wherein merging the initial non-erasure portions forms additional erasure portions that are included in the larger erasure portions.